Aleatory and Epistemic Uncertain3es. By Shahram Pezeshk, Ph.D., P.E. The university of Memphis

Transcription

1 Aleatory and Epistemic Uncertain3es By Shahram Pezeshk, Ph.D., P.E. The university of Memphis

2 Uncertainty in Engineering The presence of uncertainty in engineering is unavoidable. Incomplete or insufficient data Design must rely on predictions or estimations based on idealized models with unknown degrees of imperfection relative to reality. In practice, we might identify two broad types of uncertainty: namely, Uncertainty associated with the randomness of the underlying phenomenon that is exhibited as variability in the observed information, and Uncertainty associated with imperfect models of the real world because of insufficient or imperfect knowledge of reality. These two types of uncertainty may be called, respectively, the aleatory uncertainty and the epistemic uncertainty. The two types of uncertainty may be combined and analyzed as a total uncertainty, or treated separately. In either case, the principles of probability and statistics apply equally.

3 Aleatory Uncertainty From Alea La3n for dice This means that it represents inherent RANDOMNESS

4 Aleatory Uncertainty The aleatory (databased) uncertainty is associated with the inherent variability of basic informa3on, which is part of the real world (within our ability to observe and describe). Much of the aleatory uncertainty that civil engineers must deal with are inherent in nature and, therefore, may not be reduced or modified. On the other hand, epistemic (or knowledge- based) uncertainty is associated with imperfect knowledge of the real world, and may be reduced through applica3on of beper predic3on models and/or improved experiments. The respec3ve consequences of these two types of uncertainty may also be different the effect of the aleatory randomness leads to a calculated probability or risk, whereas the effect of the epistemic type expresses an uncertainty in the es3mated probability or risk

5 Epistemic Uncertainty This is referred to as EPISTEMIC uncertainty because it reflects our lack of knowledge.

6 Uncertainty in Engineering Finally, there should be no problem in delinea3ng between the two types of uncertainty the aleatory type is essen3ally databased, whereas the epistemic type is knowledge based. For prac3cal purposes, the epistemic uncertainty may be limited to the es3ma3on of the mean or median values, even though in theory it includes inaccuracies in the prescribed form of probability distribu3ons and in all the parameters.

7 Aleatory Uncertainty Many phenomena or processes of concern to engineers, or that engineers must contend with, contain randomness; that is, the expected outcomes are unpredictable (to some degree). Such phenomena are characterized by field or experimental data that contain significant variability that represents the natural randomness of an underlying phenomenon; i.e., the observed measurements are different from one experiment (or one observa3on) to another, even if conducted or measured under apparently iden3cal condi3ons. In other words, there is a range of measured or observed values of the experimental results; moreover, within this range certain values may occur more frequently than others. The variability inherent in such data or informa3on is sta3s3cal in nature, and the realiza3on of a specific value (or range of values) involves probability.

8 Probability Probability Likelihood of occurrence of an event rela3ve to other events A numerical measure of the likelihood of occurrence of an event within an exhaus3ve set of all possible alterna3ve events.

9 Defini7ons Random Experiment Outcome is not known un3l experiment is complete Sample Space For example flipping a coin outcome is either a head or a tail, but cannot be predicated with certainty Collec3on of all possible outcomes S={H,T} Frequency of the Event Repeat experiment n 3mes, and then count the number of 3me, f, that outcome occurred A={H} Rela3ve Frequency f/n See Table of text (Page 88), P(A) = Probability of A = ½, A={H}

10 Determinis7c Vs. Probabilis7c